This project assembles an inter-disciplinary team with an unprecedented combination of skills and experience. The team aims to build on recent advances in mathematical representation of signals, and to develop mathematical representation to the special kinds of signals occurring in Nuclear Magnetic Resonance Spectroscopy. The outcome of this team effort will be novel data representations for NMR signals that are carefully tailored to the properties of such signals, and are based on a solid mathematical foundation. Such representations will provide the NMR community with a penetrating tool for quantitative analysis and comparison of the various existing algorithms in this area, including the recent nonlinear methods such as filter diagonalization and maximum entropy methods. Such representations can also substantially improve existing NMR spectroscopy techniques, either with regards to computational speed or signal/noise separation. More ambitiously such representations may lead to innovative spectroscopic algorithms. Past experience suggests the effort will have feedback effects, with wide-spread ramifications within mathematics, and will stimulate new, intrinsic studies in this field. [unreadable] [unreadable] Inter-disciplinary research is often hampered by differing scientific languages as well as by scientific cultural barriers that separate the collaborating disciplines. Therefore, success in the effort hinges critically on having a management plan which addresses inter-disciplinary collaboration issues in a thoughtful and realistic way. The management plan of this project draws from the past experience of the team's members, and is believed to be efficient and effective. As such, the project may emerge as a model for a successful creation and management of partnerships between mathematicians and biologists, as well as for an effective approach for bridging over the aforementioned barriers. [unreadable] [unreadable]